Calculus of Variations and Geometric Measure Theory

S. Alama - L. Bronsard - R. Choksi - I. Topaloglu

Droplet breakup in the liquid drop model with background potential

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2017

ArXiv: 1708.04292 PDF


We consider a variant of Gamow's liquid drop model, with a general repulsive Riesz kernel and a long-range attractive background potential with weight $Z$. The addition of the background potential acts as a regularization for the liquid drop model in that it restores the existence of minimizers for arbitrary mass. We consider the regime of small $Z$ and characterize the structure of minimizers in the limit $Z\to 0$ by means of a sharp asymptotic expansion of the energy. In the process of studying this limit we characterize all minimizing sequences for the Gamow model in terms of "generalized minimizers".